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Class LinearOptimizationEngine

用於建立線性程式及解題的引擎。以下範例解決下列問題線性節目：

x 和 y 這兩個變數：
0 ≤ x ≤ 10
0 ≤ y ≤ 5

限制：
0 ≤ 2 * x + 5 * y ≤ 10
0 ≤ 10 * x + 3 * y ≤ 20

目標：
盡量爭取x + y

var engine = LinearOptimizationService.createEngine();

// Add variables, constraints and define the objective with addVariable(), addConstraint(), etc
// Add two variables, 0 <= x <= 10 and 0 <= y <= 5
engine.addVariable('x', 0, 10);
engine.addVariable('y', 0, 5);

// Create the constraint: 0 <= 2 * x + 5 * y <= 10
var constraint = engine.addConstraint(0, 10);
constraint.setCoefficient('x', 2);
constraint.setCoefficient('y', 5);

// Create the constraint: 0 <= 10 * x + 3 * y <= 20
var constraint = engine.addConstraint(0, 20);
constraint.setCoefficient('x', 10);
constraint.setCoefficient('y', 3);

// Set the objective to be x + y
engine.setObjectiveCoefficient('x', 1);
engine.setObjectiveCoefficient('y', 1);

// Engine should maximize the objective
engine.setMaximization();

// Solve the linear program
var solution = engine.solve();
if (!solution.isValid()) {
  Logger.log('No solution ' + solution.getStatus());
} else {
  Logger.log('Value of x: ' + solution.getVariableValue('x'));
  Logger.log('Value of y: ' + solution.getVariableValue('y'));
}

方法

方法	傳回類型	簡短說明
`addConstraint(lowerBound, upperBound)`	`LinearOptimizationConstraint`	在模型中新增線性限制。
`addConstraints(lowerBounds, upperBounds, variableNames, coefficients)`	`LinearOptimizationEngine`	將限制批次新增至模型。
`addVariable(name, lowerBound, upperBound)`	`LinearOptimizationEngine`	將新的連續變數新增至模型。
`addVariable(name, lowerBound, upperBound, type)`	`LinearOptimizationEngine`	將新變數新增至模型。
`addVariable(name, lowerBound, upperBound, type, objectiveCoefficient)`	`LinearOptimizationEngine`	將新變數新增至模型。
`addVariables(names, lowerBounds, upperBounds, types, objectiveCoefficients)`	`LinearOptimizationEngine`	將變數批次新增至模型。
`setMaximization()`	`LinearOptimizationEngine`	設定最佳化方向，盡可能提升線性目標函式。
`setMinimization()`	`LinearOptimizationEngine`	設定最佳化方向，盡可能降低線性目標函式。
`setObjectiveCoefficient(variableName, coefficient)`	`LinearOptimizationEngine`	設定線性目標函式中的變數係數。
`solve()`	`LinearOptimizationSolution`	以預設期限 30 秒為目前的線性程式求解。
`solve(seconds)`	`LinearOptimizationSolution`	解開目前的線性程式。

內容詳盡的說明文件

`addConstraint(lowerBound, upperBound)`

在模型中新增線性限制。限制的上限和下限如下建立容器變數係數是透過呼叫 LinearOptimizationConstraint.setCoefficient(variableName, coefficient) 來定義。

var engine = LinearOptimizationService.createEngine();

// Create a linear constraint with the bounds 0 and 10
var constraint = engine.addConstraint(0, 10);

// Create a variable so we can add it to the constraint
engine.addVariable('x', 0, 5);

// Set the coefficient of the variable in the constraint. The constraint is now:
// 0 <= 2 * x <= 5
constraint.setCoefficient('x', 2);

參數

名稱	類型	說明
`lowerBound`	`Number`	限制下限
`upperBound`	`Number`	限制條件上限

回攻員

LinearOptimizationConstraint：已建立限制

`addConstraints(lowerBounds, upperBounds, variableNames, coefficients)`

將限制批次新增至模型。

var engine = LinearOptimizationService.createEngine();

// Add a boolean variable 'x' (integer >= 0 and <= 1) and a real (continuous >= 0 and <= 100)
variable 'y'.
engine.addVariables(['x', 'y'], [0, 0], [1, 100],
    [LinearOptimizationService.VariableType.INTEGER,
        LinearOptimizationService.VariableType.CONTINUOUS]);

// Adds two constraints:
//   0 <= x + y <= 3
//   1 <= 10 * x - y <= 5
engine.addConstraints([0.0, 1.0], [3.0, 5.0], [['x', 'y'], ['x', 'y']], [[1, 1], [10, -1]]);

參數

名稱	類型	說明
`lowerBounds`	`Number[]`	限制的下限
`upperBounds`	`Number[]`	限制條件的上限
`variableNames`	`String[][]`	要設定係數的變數名稱
`coefficients`	`Number[][]`	設定係數

回攻員

LinearOptimizationEngine：線性最佳化引擎

`addVariable(name, lowerBound, upperBound)`

將新的連續變數新增至模型。變數是以其名稱參照。類型已設為 VariableType.CONTINUOUS。

var engine = LinearOptimizationService.createEngine();
var constraint = engine.addConstraint(0, 10);

// Add a boolean variable (integer >= 0 and <= 1)
engine.addVariable('x', 0, 1, LinearOptimizationService.VariableType.INTEGER);

// Add a real (continuous) variable. Notice the lack of type specification.
engine.addVariable('y', 0, 100);

參數

名稱	類型	說明
`name`	`String`	指定變數的專屬名稱
`lowerBound`	`Number`	變數下限
`upperBound`	`Number`	變數上限

回攻員

LinearOptimizationEngine：線性最佳化引擎

`addVariable(name, lowerBound, upperBound, type)`

將新變數新增至模型。變數是以其名稱參照。

var engine = LinearOptimizationService.createEngine();
var constraint = engine.addConstraint(0, 10);

// Add a boolean variable (integer >= 0 and <= 1)
engine.addVariable('x', 0, 1, LinearOptimizationService.VariableType.INTEGER);

// Add a real (continuous) variable
engine.addVariable('y', 0, 100, LinearOptimizationService.VariableType.CONTINUOUS);

參數

名稱	類型	說明
`name`	`String`	指定變數的專屬名稱
`lowerBound`	`Number`	變數下限
`upperBound`	`Number`	變數上限
`type`	`VariableType`	變數類型，可以是 `VariableType`

回攻員

LinearOptimizationEngine：線性最佳化引擎

`addVariable(name, lowerBound, upperBound, type, objectiveCoefficient)`

將新變數新增至模型。變數是以其名稱參照。

var engine = LinearOptimizationService.createEngine();
var constraint = engine.addConstraint(0, 10);

// Add a boolean variable (integer >= 0 and <= 1)
engine.addVariable('x', 0, 1, LinearOptimizationService.VariableType.INTEGER, 2);
// The objective is now 2 * x.

// Add a real (continuous) variable
engine.addVariable('y', 0, 100, LinearOptimizationService.VariableType.CONTINUOUS, -5);
// The objective is now 2 * x - 5 * y.

參數

名稱	類型	說明
`name`	`String`	指定變數的專屬名稱
`lowerBound`	`Number`	變數下限
`upperBound`	`Number`	變數上限
`type`	`VariableType`	變數類型，可以是 `VariableType`
`objectiveCoefficient`	`Number`	變數的客觀係數

回攻員

LinearOptimizationEngine：線性最佳化引擎

`addVariables(names, lowerBounds, upperBounds, types, objectiveCoefficients)`

將變數批次新增至模型。這些變數是用名稱所參照。

var engine = LinearOptimizationService.createEngine();

// Add a boolean variable 'x' (integer >= 0 and <= 1) and a real (continuous >=0 and <= 100)
// variable 'y'.
engine.addVariables(['x', 'y'], [0, 0], [1, 100],
    [LinearOptimizationService.VariableType.INTEGER,
        LinearOptimizationService.VariableType.CONTINUOUS]);

參數

名稱	類型	說明
`names`	`String[]`	指定變數的專屬名稱
`lowerBounds`	`Number[]`	變數的下限
`upperBounds`	`Number[]`	變數上限
`types`	`VariableType[]`	變數類型，可以是 `VariableType`
`objectiveCoefficients`	`Number[]`	變數的客觀係數

回攻員

LinearOptimizationEngine：線性最佳化引擎

`setMaximization()`

設定最佳化方向，盡可能提升線性目標函式。

var engine = LinearOptimizationService.createEngine();

// Add a real (continuous) variable. Notice the lack of type specification.
engine.addVariable('y', 0, 100);

// Set the coefficient of 'y' in the objective.
// The objective is now 5 * y
engine.setObjectiveCoefficient('y', 5);

// We want to maximize.
engine.setMaximization();

回攻員

LinearOptimizationEngine：線性最佳化引擎

`setMinimization()`

設定最佳化方向，盡可能降低線性目標函式。

var engine = LinearOptimizationService.createEngine();

// Add a real (continuous) variable. Notice the lack of type specification.
engine.addVariable('y', 0, 100);

// Set the coefficient of 'y' in the objective.
// The objective is now 5 * y
engine.setObjectiveCoefficient('y', 5);

// We want to minimize
engine.setMinimization();

回攻員

LinearOptimizationEngine：線性最佳化引擎

`setObjectiveCoefficient(variableName, coefficient)`

設定線性目標函式中的變數係數。

var engine = LinearOptimizationService.createEngine();

// Add a real (continuous) variable. Notice the lack of type specification.
engine.addVariable('y', 0, 100);

// Set the coefficient of 'y' in the objective.
// The objective is now 5 * y
engine.setObjectiveCoefficient('y', 5);

參數

名稱	類型	說明
`variableName`	`String`	設定係數的變數名稱
`coefficient`	`Number`	客觀函數中的變數係數

回攻員

LinearOptimizationEngine：線性最佳化引擎

`solve()`

以預設期限 30 秒為目前的線性程式求解。傳回找到的解決方案。

var engine = LinearOptimizationService.createEngine();

// Add variables, constraints and define the objective with addVariable(), addConstraint(), etc
engine.addVariable('x', 0, 10);

// ...

// Solve the linear program
var solution = engine.solve();
if (!solution.isValid()) {
  throw 'No solution ' + solution.getStatus();
}
Logger.log('Value of x: ' + solution.getVariableValue('x'));

回攻員

LinearOptimizationSolution - 最佳化解決方案

`solve(seconds)`

解開目前的線性程式。傳回找到的解決方案。如果這是最佳方案解決方案

var engine = LinearOptimizationService.createEngine();

// Add variables, constraints and define the objective with addVariable(), addConstraint(), etc
engine.addVariable('x', 0, 10);

// ...

// Solve the linear program
var solution = engine.solve(300);
if (!solution.isValid()) {
  throw 'No solution ' + solution.getStatus();
}
Logger.log('Value of x: ' + solution.getVariableValue('x'));

參數

名稱	類型	說明
`seconds`	`Number`	解決問題的期限 (以秒為單位)最長期限為 300 秒

回攻員

LinearOptimizationSolution - 最佳化解決方案